Question

1. $(2x^{-1})^4$

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$, so $(2x^{-1})^4 = 2^4 \cdot (x^{-1})^4$

Step2: Calculate the constant term

$2^4 = 16$

Step3: Apply power of a power rule

$(x^m)^n = x^{m \cdot n}$, so $(x^{-1})^4 = x^{-1 \times 4} = x^{-4}$

Step4: Rewrite with positive exponent

$x^{-4} = \frac{1}{x^4}$

Answer:

$\frac{16}{x^4}$